A simple shear model based upon the mechanical theory of dislocation fields was developed in order to predict in a straightforward way the effects of channel width on the kinematic hardening of a soft–hard periodic composite material with channel-type microstructures. The model used a continuous description of the crystal incompatibility at channel–wall interfaces. A non-local tangential continuity condition on the plastic distortion rate was applied, accounting for the conservation of the Burgers vector at the interfaces. The constraints thus imposed on plasticity at the walls enhance kinematic hardening, which was found to be channel-size dependent for a fixed refined mesh size. The smaller the channel width became for a given volume fraction of walls (hard phase), the stronger the kinematic hardening and the Bauschinger effect. When the channel width was sufficiently large or when the continuous treatment of interfaces was overlooked, the model became equivalent to a size-independent isostrain mean field approach, which was only able to retrieve hard-phase volume fraction effects on composite hardening. Due to dislocation density transport, the incompatibility in the plastic distortion between phases was accommodated by the creation of a continuous layer of polar edge dislocation density through a gradual dynamic accumulation at the channel–wall interfaces. In contrast, the singular surface dislocations at the channel–wall interfaces commonly observed in Eshelby-type mean field approaches were shown to be unable to describe size-dependent hardening.

Size Effects on the Hardening of Channel-Type Microstructures: a Field Dislocation Mechanics-Based Approach. V.Taupin, S.Berbenni, C.Fressengeas: Acta Materialia, 2012, 60[2], 664-73